Yankees fans have been crushing A-Rod for years -- some say he's overpaid, some say he's overrated, some just like to give him grief -- but now that the famous third baseman is smack in the crosshairs of ANOTHER steroid investigation, the opprobrium has reached new levels.

But Giuliani tells us, it has to stop now -- "I was one of the first to say that Yankee fans should not boo A-Rod. He's on our team. You gotta root for him. I think he's one of the greatest players ever."

For the record, A-Rod admitted to using banned substances from 2001 to 2003 ... but he was never punished by MLB.